Wrinkled Flame Front Research Articles

Integral equation approach for analyzing acoustic interactions with wrinkled flame fronts

Flame-acoustic wave interactions play an important role in the characteristic unsteadiness of turbulent combustion processes. They arise because acoustic waves incident from other parts of the flame or from external sources impinge upon the flame and are scattered because of the significant change in sound speed and density at the flame front. The characteristics of the scattered waves are complex, due to the fact that they are interacting with a dynamic flame surface that is convoluted over a broad range of length and time scales. Over a wide range of frequencies (e.g., up to about 20 kHz), such turbulent flames may be treated as nonpassive (i.e., the flame acts as a source of acoustic energy) temperature discontinuities. We describe here an integral equation approach, similar to the development of the Ffowcs Williams–Hawking (FWH) equation, that is suitable for analysis of acoustic-flame interactions. This FWH equation is generalized for the case of interest where the surface is penetrable, not passive, and whose area varies in time. The integration surface consists of the time varying flame front that divides two homogeneous regions. The wave motions in these two regions are coupled by appropriate mass, momentum, and energy conservation conditions.

Analysis of acoustic wave interactions with turbulent premixed flames

This paper analyzes acoustic wave interactions with turbulent, premixed flames. It generalizes a previousstudy that treated the flame as a passive temperature discontinuity by accounting for the effects of pressure disturbances upon the mass burning rate. Similar to the prior study the problem is posed with an integral formulation of the wave equation and assumes that the local flame front curvature is much larger than the acoustic wavelength. Thus, it is most appropriate for considering interactions between flames and short-wavelength (e.g., high-frequency) disturbances. The analysis includes such factors as the response of the mass burning rate to acoustic perturbations, the temperature change across the flame, and the geometric complexities of the evolving, wrinkled front. Explicit solutions are derived for the coherent field, showing that its characteristics are controlled by the wavelength of the disturbance, the probability density function of the flame front position and orientation, the incident wave angle, the temperature jump across the flame, and the response of the mass burning rate to acoustic perturbations. These results suggest that several differences exist between the characteristics of waves scattered from laminar and turbulent flames. With increased flame front wrinkling, the coherent field becomes increasingly independent of the temperature jump across the flame and response of the mass burning rate. This result contrasts with the strong importance of these parameters in laminar-flame-acoustic-wave interaction problems. In addition, results show that the wrinkled characteristics of turbulent flames shift the phase and reduce the amplitude of the coherent field relative to its value if the flame front were smooth: that is, they serve as a source of damping of coherent acoustic energy. This damping source is particularly significant for disturbances whose wave-lengths are on the order of or smaller than the characteristic scales of flame wrinkling.

Flame/Flow Interaction in Oscillating Flow Field

A numerical study on the premixed wrinkled flame front has been conducted in order to examine the motion of the wrinkled flame front and flame/flow interaction in an oscillating flow field. The conventional G-equation is solved to determine the time dependent behavior of the flame front by using a model in which the flame front is regarded as a source of volume and vorticity. To confirm the numerical simulation, the response of the wrinkled premixed flame under the oscillating flow field is experimentally observed. The experimental results, where flame/flow interaction is clearly observed, can be depicted by the numerical analysis. The wrinkled region of the flame front hardly responds to the upstream flow oscillation even if this oscillation is as large as the mean velocity of the flow field. The behavior of the wrinkled flame front is found to result from flame/flow interaction due to volume expansion and vorticity production at the flame front. Especially in a time varying flow field, vorticity production plays a decisive role in the motion of the wrinkled region of the flame front by counteracting the oscillating flow field.

Flame front surface characteristics in turbulent premixed propane/air combustion

The characteristics of the flame front surfaces in turbulent premixed propane/air flames were investigated. Flame front images were obtained using laser-induced fluorescence (LIF) of OH and Mie scattering on two Bunsen–type burners of 11.2-mm and 22.4-mm diameters. Nondimensional turbulence intensity, u′/ S L , was varied from 0.9 to 15, and the Reynolds number, based on the integral length scale, varied from 40 to 467. Approximately 100 images were recorded for each experimental condition. Fractal parameters (fractal dimension, inner and outer cutoffs) and corresponding standard deviations were determined by analysis of the flame front images using the caliper technique. The fractal dimensions derived from OH and Mie scattering images are almost identical. However, inner and outer cutoffs from OH images are consistently higher than those obtained from Mie scattering. The self-similar region of the flame front wrinkling is about a decade for all flames studied. In the nondimensional turbulence intensity range from 1 to 15, it was found that the mean fractal dimension is about 2.2 and it does not show any dependence on turbulence intensity. This contradicts the findings of the previous studies that showed that the fractal dimension asymptotically reaches to 2.35–2.37 when the nondimensional turbulence intensity u′/ S L exceeds 3. It is shown that the reason for this discrepancy is the image analysis method used in the previous studies. Examples are given to show the inadequacy of the circle method used in previous studies for extraction of fractal parameters from flame front images. The fractal parameters obtained so far, in this and previous studies, are not capable of correctly predicting the turbulent burning velocity using the available fractal area closure model.

Premixed-flame propagation in turbulent Taylor–Couette flow

Turbulent-flame speeds in methane–air mixtures were measured in a Taylor–Couette apparatus with counter-rotating cylinders, used to generate turbulence that is nearly homogeneous and isotropic over many integral length and time scales. While laminar-flame propagation is found to be influenced by the Darrieus–Landau instability and heat loss to the walls of the apparatus, turbulent-flame propagation in high-intensity turbulence is found to be uninfluenced by these effects. A decreasing sensitivity of the turbulent-flame speed to increases in turbulence intensity is found to occur beyond turbulence intensities of approximately 2.5 times the laminar-flame speed. This is possibly due to a transition to a nonflamelet combustion regime where flame propagation is influenced by both small-scale flame-structure modification and large-scale flame-front wrinkling. Results are compared with those obtained by earlier investigators using other experimental apparatuses and with theoretical predictions.

Effects of Swirl on High-Speed Combustion in a Single-Shot Optical SI Engine

Single-shot tests in a single-cylinder, optical SI engine operated by a rapid compression and expansion machine were performed in order to investigate the combined effects of engine speed, ignition position and swirl on early combustion and overall performance. For central ignition, swirl showed consistently favourable effects on combustion-related performance. However, at half-radius ignition the desirable swirl effect persisted at low engine speeds but faded away as the speed increased. This reversing of trends can be partially explained by differences in the maximum cylinder pressure, flame growth rate and flame front wrinkling.

Existence of planar flame fronts in convective-diffusive periodic media

We prove the existence of planar travelling wave solutions in a reaction-diffusion-convection equation with combustion nonlinearity and self-adjoint linear part in Rn, n≧1. The linear part involves diffusion-convection terms and periodic coefficients. These travelling waves have wrinkled flame fronts propagating with constant effective speeds in periodic inhomogeneous media. We use the method of continuation, spectral theory, and the maximum principle. Uniqueness and monotonicity properties of solutions follow from a previous paper. These properties are essential to overcoming the lack of compactness and the degeneracy in the problem.

The spatial scalar structure of premixed turbulent stagnation point flames

A high speed tomographic technique is used to quantify the spatial scalar structure of stagnation flow stabilized premixed flames. Studies are performed on CH{sub 4}/Air and C{sub 2}H{sub 4}/Air turbulent flames with equivalence ratios ranging from 0.75 to 1.0. The gas velocity at the nozzle exit is 5 m/s, the turbulence intensity is 7%, the integral length scale 3 mm and hence the turbulence Reynolds number is 70. The light source is a copper vapor laser which produces 20 ns, 5 mJ pulses at a 4 KHz repetition rate. Cylindrical lenses transform the 38 mm circular laser beam to a sheet 50 mm high and 0.6 mm thick. A high speed Fastax camera is used to record the tomographic images formed by the scattering of light from oil droplets seeded in the reactant flow which disappear at the flame front. The films are digitized and the wrinkled flame front extracted from the images by a thresholding technique. The integral scalar length scales proposed in the model of Bray-Champion-Libby are deduced from the tomographic movies by numerically constructing flame crossing sequences from the burned and unburned probability density functions of flame crossing length and performing a spectral analysis of these sequences.more » The integral scalar length scales are found to be similar to the integral length scales of the incident turbulence. A fractal analysis was performed on the flame boundaries to characterize the flame geometry and provide from an estimate of the flame surface area a measure of the turbulent burning rate. The flame area increase is found to underestimate the turbulent burning velocity when compared with direct measurements of the flow velocity at the cold boundary. 12 refs., 2 tabs.« less

Investigation of extinction in unsteady flames in turbulent combustion by 2D-LIF of OH radials and flamelet analysis

An experimental and theoretical investigation of premixed turbulent combustion in an engine simulator is presented. The distribution of hydroxyl radicals formed in the combustion of propane/air mixtures was visualized by 2D-LIF and used to monitor the progress of the combustion process. For stoichiometric mixtures, images showed a continuous wrinkled flame front, while in lean (λ=1.5) mixtures, local flame extinction was observed as discontinuities in the reaction zone. A bright active reaction zone was still observed in flame inlets and closed concave structures. The effects of self-absorption and of collisional quenching on the fluorescence signal are considered and appear to have only a minor net influence on the shape and width of the flame front. The images are evaluated and interpreted in terms of the Lewis number effect and the laminar flamelet model. Analysis was performed by determining the contour lines of the images (specifically, the ratios of average maximum to equilibrium OH concentration) and comparing with corresponding ratios from unstrained flame simulations. The results show that although the degree of turbulence is not high enough for straining effects to be important, flamelet curvature does play a significant role in the combustion of lean mixtures; this is manifested by a mean effective flame velocity that is less than the laminar burning velocity.

Flame initiation in lean, quiescent and turbulent mixtures with various igniters

High speed flame photographs have been taken, following ignition, in an explosion bomb, equipped with four high speed fans to create turbulence. The different igniters studied, under quiescent and turbulent conditions of the the lean methane-air mixture, comprised o (i) a conventional two electrode spark system (ii) a surface discarge spark (iii) a plasma jet (iv) a plasma jet with wetted cavity (v) a torch from a pre-chamber Hot kernel volume, flame front wrinkling and flame speed were measured during the early stages of flame development. Systems (ii) to (v) were potentially superior to (i) in their ability to create a larger igniting volume of hot, reactive gas. The flame speeds for systems (iii) to (v) were enhanced by jet-generated turbulence and, additionally, by active species in the case of the plasma jet. In turbulent mixtures, after a few milliseconds the flame speed is predominantly a function of the turbulence. Ignition limits have been measured over a range of r.m.s. turbulent velocities and different igniters compared. With limit mixtures, the ratio of chemical to eddy lifetime is a useful correlating parameter. Ignition limits for the different igniters fall within an upper bound for flame propagation defined by a fixed value of this ratio.

Application of pole decomposition to an equation governing the dynamics of wrinkled flame fronts

Application of pole decomposition to an equation governing the dynamics of wrinkled flame fronts

A Calculation of Wrinkled Flames

Abstract In an earlier work, Sivashinsky derived a nonlinear integro-differential equation for spontaneous hydrodynamic instability of a plane flame front. The simplified form of that equation which describes a1 steady progressive wave of long period is reconsidered here. It is shown to represent a wrinkled flame front whose slope has a logarithmic singularity at each wrinkle. We have computed the flame profile and its speed of propagation more accurately than done previously by Michelson and Sivashinksy, and find that the increase in propagation speed due to wrinkling is in surprisingly good agreement with recent experimental findings.

Velocity-temperature correlation in premixed flame

The velocity and the temperature were measured simultaneously with a laser Doppler anemometer and a compensated thermocouple, respectively, in the turbulent premixed flame, and their cross-correlation was calculated with a microcomputer. A seed deposition effect of the thermocouple on the cross-correlation coefficient was avoided by compensating for the temperature signal with a somewhat larger time constant than the theoretical value. The effect on the cross-correlation of separating of the measuring control volume of LDA and the thermocouple placed on the downstream side was also investigated. Though a small separation of the thermocouple downstream from the measuring control volume had little effect, the shift of radial direction had a severe effect. The axial velocity-temperature correlation gave large negative values in the whole region where the gradient of mean temperaturealong the axial direction δ/δ x was positive. This fact corresponds to the normal turbulent heat transfer and can be explained by a mechanism whereby temperature fluctuation is induced by velocity fluctuation. However, the radial velocity-temperature correlation showed positive values in the vicinity of the flame front where the radial temperature gradient η/δ r was still positive. This corresponds to an abnormal turbulent heat transport phenomenon. To clarify this phenomenon, the probability density functions and the macroscale of the velocity and the temperature fluctuations were also measured. The bimodal nature of the PDF appeared at the flame front in all fluctuating components, which suggests that the flame front structure of the flame studied was approximated by the wrinkled flame model. Abnormal turbulent heat transfer can be explained by the wrinkled flame front structure or the fluctuation of the heat generated at the measuring point, and cannot be neglected in the modeling of the combustion.